scholarly journals Representation formula and bi-Lipschitz continuity of solutions to inhomogeneous biharmonic Dirichlet problems in the unit disk

2017 ◽  
Vol 456 (2) ◽  
pp. 1150-1175 ◽  
Author(s):  
Peijin Li ◽  
Saminathan Ponnusamy
Keyword(s):  
Unit Disk ◽  
Lipschitz Continuity ◽  
Representation Formula ◽  
Dirichlet Problems ◽  
Continuity Of Solutions

scholarly journals Lipschitz Continuity for the Solutions of Triharmonic Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Zhou Yu ◽  
Xiao Bing
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Dirichlet Boundary ◽  
Lipschitz Continuity ◽  
Boundary Value ◽  
Jordan Domain ◽  
Lipschitz Continuous ◽  
Equivalent Conditions

Let D be the unit disk in the complex plane C and denote T=∂D. Write Hom+T,∂Ω for the class of all sense-preserving homeomorphism of T onto the boundary of a C2 convex Jordan domain Ω. In this paper, five equivalent conditions for the solutions of triharmonic equations ∂z∂z¯3ω=ff∈CD¯ with Dirichlet boundary value conditions ωzz¯zz¯T=γ2∈CT,ωzz¯T=γ1∈CT and ωT=γ0∈Hom+T,∂Ω to be Lipschitz continuous are presented.

FRACTIONAL DEGREE VORTICES FOR A SPINOR GINZBURG–LANDAU MODEL

2006 ◽  
Vol 08 (03) ◽  
pp. 355-380 ◽  
Author(s):  
STAN ALAMA ◽  
LIA BRONSARD
Keyword(s):  
High Temperature ◽  
Unit Disk ◽  
High Temperature Superconductors ◽  
Dirichlet Problems ◽  
Complex Vector ◽  
Ginzburg Landau ◽  
Landau Model ◽  
Physics Literature ◽  
Bose Einstein ◽  
Vector Valued

Recent papers in the physics literature have introduced spin-coupled (or spinor) Ginzburg–Landau models for complex vector-valued order parameters in order to account for ferromagnetic or antiferromagnetic effects in high-temperature superconductors and in optically confined Bose–Einstein condensates. In this paper, we show that such models give rise to new types of vortices, with fractional degree and nontrivial core structure. We illustrate the various possibilites with some specific examples of Dirichlet problems in the unit disk.

QUASICONFORMAL SOLUTIONS OF POISSON EQUATIONS

2015 ◽  
Vol 92 (3) ◽  
pp. 420-428 ◽  
Author(s):  
PEIJIN LI ◽  
JIAOLONG CHEN ◽  
XIANTAO WANG
Keyword(s):  
Unit Disk ◽  
Poisson Equation ◽  
Lipschitz Continuity ◽  
Poisson Equations ◽  
The Poisson Equation

The main aim of this paper is to establish the Lipschitz continuity of the $(K,K^{\prime })$-quasiconformal solutions of the Poisson equation ${\rm\Delta}w=g$ in the unit disk $\mathbb{D}$.

scholarly journals NONLINEAR MEAN-VALUE FORMULAS ON FRACTAL SETS

Fractals ◽  
2018 ◽  
Vol 26 (06) ◽  
pp. 1850091
Author(s):  
J. C. NAVARRO ◽  
J. D. ROSSI
Keyword(s):  
Comparison Principle ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Lipschitz Continuity ◽  
Continuous Solution ◽  
Sierpinski Gasket ◽  
Mean Value ◽  
Fractal Sets ◽  
Continuity Of Solutions ◽  
The Mean

In this paper we study the solutions to nonlinear mean-value formulas on fractal sets. We focus on the mean-value problem [Formula: see text] in the Sierpiński gasket with prescribed values [Formula: see text], [Formula: see text] and [Formula: see text] at the three vertices of the first triangle. For this problem we show existence and uniqueness of a continuous solution and analyze some properties like the validity of a comparison principle, Lipschitz continuity of solutions (regularity) and continuous dependence of the solution with respect to the prescribed values at the three vertices of the first triangle.

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